no. 2
Minimal redundant digit expansions in the gaussian integers
Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 517-528.

Un résultat récent établit qu’il suffit de connaître les deux derniers chiffres significatifs du développement en base q usuel d’un entier pour calculer le dernier chiffre significatif dans le développement en base q redondant minimal. Nous montrons que l’énoncé analogue pour les entiers de Gauss est faux.

We consider minimal redundant digit expansions in canonical number systems in the gaussian integers. In contrast to the case of rational integers, where the knowledge of the two least significant digits in the “standard” expansion suffices to calculate the least significant digit in a minimal redundant expansion, such a property does not hold in the gaussian numbers : We prove that there exist pairs of numbers whose non-redundant expansions agree arbitrarily well but which have different least significant digits in minimal redundant expansions.

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     title = {Minimal redundant digit expansions in the gaussian integers},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {517--528},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     year = {2002},
     mrnumber = {2040691},
     zbl = {1076.11005},
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     url = {http://www.numdam.org/item/JTNB_2002__14_2_517_0/}
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Heuberger, Clemens. Minimal redundant digit expansions in the gaussian integers. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 517-528. http://www.numdam.org/item/JTNB_2002__14_2_517_0/

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